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. 2022 Jul 26;29(60):91105–91126. doi: 10.1007/s11356-022-22147-0
Indices
R Set of raw materials (RMs) indexed by r
S Set of suppliers indexed by s
I Set of manufacturers indexed by i
J Set of DCs indexed by j
K Set of customers indexed by k
C Set of CCs indexed by c
Q Set of RECs indexed by q
H Set of SMs indexed by h
B Set of RCCs indexed by b
D Set of disposal centers indexed by d
T Set of manufacturing technologies indexed by t
N Set of countries in which international suppliers are located indexed by n
F Set of information-sharing systems (ISS) indexed by f
Parameters
SFsn Cost of contracting with supplier s located country n
MFXit Fixed-Cost (FC) of opening manufacturer i by technology t
DFXj FC of opening DC j
CFXc FC of opening CC c
RFXq FC of opening REC q
BFXb FC of opening RCC b
IFXf FC of establishing ISS f
RPCrs Cost of buying raw material r from supplier s located in country n
MCit Manufacturing cost for technology t in manufacturer i
DOCj Operation costs of DC j
COCc Operation costs of CC c
CORq Cost of repairing products in REC q
COBb Cost of recycling components in RCC b
SHC The shortage cost
CDRrn Customs duty rate of RM r supplied from a supplier located in country n (it is equal to zero for the domestic suppliers)
EXRn Exchange rate of the currency of country n (it is equal to 1 for the domestic suppliers)
TC Unit of transportation cost
SMPh The selling price of components in SM h
pr The selling price for recycled material
SCsnr The capacity of supplier s located in country n for RM r
MCit The capacity of manufacturer i with technology t
CDCj The capacity of DC j
CPCc The capacity of CC c
CPRq The capacity of REC q
CPBb The capacity of RCC b
DMPk The demand of customers k
disee Distance between facility e and facility e;e,es,i,j,k,c,d,h,q,b
σr The utilization rate of raw material r in the product
φk Rate of return of products for customers k
β The percentage of the repairable returned products
δ The percentage of components that are successfully recycled
ω The quantity of materials obtained from recycling the product
MEit Carbon emission due to the manufacturing process in manufacturer i using technology t
REq Carbon emission due to the repairing process in REC q
BEb Carbon emission due to the recycling process in RCC b
TE Carbon emission due to the transportation process
JCe The job opportunity created by establishing a facility es,i,j,c,q,b
IEf The percent of the information that can be exchanged in the whole SC network using ISS f
Decision variables
SZsn A binary variable that shows whether supplier s located country n is selected or not
MZit A binary variable that shows whether manufacturer i with technology t is opened or not
DZj A binary variable that shows whether DC j is opened or not
CZc A binary variable that shows whether CC c is opened or not
RZq A binary variable that shows whether REC q is opened or not
BZb A binary variable that shows whether RCC b is opened or not
IZf A binary variable that shows whether ISS f is established or not
ZSMrsni The quantity of RM r sent from supplier s located in country n to manufacturer i
ZMDijt The quantity of product sent from manufacturer i with technology t to DC j
ZDPjk The quantity of product sent from DC j to customers k
ZDCkc The quantity of returned product sent from customers k to CC c
ZCRcq The quantity of products sent from CC c to REC q
ZCBcb The quantity of products sent from CC c to RCC b
ZRSqh The quantity of repaired products sent from REC q to SM h
ZBDbd The quantity of wastes sent from RCC b to disposal center d
ZBSbsn The quantity of recycled materials sent from RCC b to supplier s located in country n
KMKk The quantity of shortage for the customers k
VSIf The quantity of visibility of information in the supply chain networks when ISS f is established
α The service level